I'll combine my responses to Richard's three previous messages;
Richard wrote:
>Although I think you are looking for a mathematical solution, and I do
>believe one is
>possible, I don't think one is needed (though it would be an interesting
>derivation).
>I would vote A only without the need to refer to any math. The
I'm not necessarily looking for a mathematical solution. The point is that,
even given a significant amount of information on which to base one's vote,
it is still difficult to divine how to vote in approval. So far, two
people, both highly intelligent and with a thorough understanding of voting
systems, have decided to vote in two separate ways, given the same
information, preferences and expected utility outcomes. I suspect the rest
of the list would be similarly divided, if not the populace as a whole.
>If the scenario happens under approval voting, I don't think that it
happens
>for the wrong reasons. The result happens because enough voters felt the
>utility gap between their favorite candidate and their second favorite (or
>their second and third, or whatever) was small enough to include that
>additional choice, while the utility gap to their next choice was larger.
In
>other words, approval is tending to maximize voter utility.
If people, given exactly the same utilities, cast totally different approval
ballots, then I don't see how Approval can maximise voter utility in any
even handed manner. Any utility (in a broader sense) advantage Approval has
over Condorcet is more than countenanced by the fact that it doesn't give
votes equal power. This is also true, of course, if someone votes
insincerely (and non-strategically) or truncates their vote in a Condorcet
election, but this inequality is the fault of the voter. The inequality in
Approval is the fault of the voting system.
>Approval counts more than one preference. If there are four candidates, and
>I vote AB, then I am expressing the following preferences:
>
>A > C
>B > C
>A > D
>B > D
If A is your favourite, B is your lesser of two evils candidate and C is the
greater of two evils candidate, you cannot express your A>B preference as
well as your B>C preference. You have to pick one, and if you make the
wrong choice, your candidate can lose. In a Condorcet election, there can
be strategies involved, but they are complex and diffuse enough so that,
without highly detailed information, it is safest to number all your
preferences in sincere order. The only choice you have to make in making
your vote as effective as is possible, is who you like the best.
